# [Statlist] Seminar ueber Statistik

Christina Kuenzli kuenzli at stat.math.ethz.ch
Thu Nov 23 14:07:59 CET 2006

```              ETH and University of Zurich

Proff.
A.D. Barbour - P. Buehlmann - F. Hampel
H.R. Kuensch - S. van de Geer

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We are glad to announce the following talk
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Friday, December 1st, 2006, 15.15, LEO C 6

Collecting a batch of items on a warehouse carousel
Willem R. van Zwet, University of Leiden

A carousel is an automated storage and retrieval system that is
widely used in modern warehouses. The system consists of a circular disk
with a large number of shelves or drawers along its circumference. The
disk can rotate in either direction past a picker who has a list of items
to be collected from n different drawers. We model this process by
assuming that the picker occupies a fixed position along a circle and
that the n drawers to be visited are distributed independently and
uniformly along the circle. The picker will take the shortest route from
his starting position past each of the n drawers, possibly reversing the
direction of the movement during the process. We determine the
probability distribution of the length of the shortest route and discuss
its limiting behaviour for large n. Along the way, we encounter a rather
curious property of exponentially distributed random variables and a
probability distribution of a most unusual kind. Of course this study
merely provides a starting point for a discussion of many other
interesting and difficult practical problems connected with warehouse
carousels. The talk describes joint work with Nelly Litvak.

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Christina Kuenzli            <kuenzli at stat.math.ethz.ch>
Seminar fuer Statistik
Leonhardstr. 27,  LEO D11      phone: +41 (0)44 632 3438
ETH-Zentrum,                   fax  : +41 (0)44 632 1228
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~

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